Question

name the two pairs of vertical angles in the figure. ∠1 and ∠3 ∠2 and ∠4 m∠1 = 104°. find the remaining three angle measures. m∠2 = ° m∠3 =? ° m∠4 =? °

Explanation:

Step1: Use the property of adjacent angles

Adjacent angles on a straight line sum to \(180^{\circ}\). So, \(m\angle1 + m\angle2=180^{\circ}\). Given \(m\angle1 = 104^{\circ}\), then \(m\angle2=180^{\circ}- 104^{\circ}\).

$$m\angle2 = 76^{\circ}$$

Step2: Use the property of vertical angles

Vertical angles are equal. Since \(\angle1\) and \(\angle3\) are vertical angles, \(m\angle3=m\angle1\). So, \(m\angle3 = 104^{\circ}\).

Step3: Use the property of vertical angles again

Since \(\angle2\) and \(\angle4\) are vertical angles, \(m\angle4=m\angle2\). So, \(m\angle4 = 76^{\circ}\).

Answer:

\(m\angle2 = 76^{\circ}\), \(m\angle3 = 104^{\circ}\), \(m\angle4 = 76^{\circ}\)